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3.3 Properties of Logarithms

Learn how to apply logarithmic properties effectively, including change of base formula and expanding/condensing log functions. Improve your skills with detailed examples and explanations.

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3.3 Properties of Logarithms

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  1. 3.3 Properties of Logarithms Change of base formula loga x = or

  2. Ex. log4 30 = 2.4534 3.8074 log2 14 = Properties of Logarithms 1. loga (uv) = loga u + loga v 1. ln(uv) = ln u + ln v 2. log u/v = loga u – loga v 2. ln u/v = ln u – ln v 3. loga un = n loga u 3. ln un = n ln u

  3. Use the logarithmic properties to expand the following. log10 5x3y = log 5 + log x3 + log y = log 5 + 3log x + log y ln (3x – 5)1/2 – ln 7 ln 1 – (ln x + ln y) = - ln x – ln y 0

  4. Condensing a log function 2 ln (x + 6) + ln x = ln x(x + 6)2 ln x - ln y + ln z =

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